Early spring is the best time to divide and separate Shasta daisy (Leucanthemum x superbum), but it is an extremely tough perennial and can be moved or divided almost any time of year. Avoid dividing it during hot, dry periods of midsummer, however. Shasta daisy usually needs to be divided every few years to maintain its vigor.
If the central portion of the clump begins to die out, it's a good indication that it's time to divide the plant. Dig up the entire clump, then slice through it with a sharp spade to make new plants. As long as the division has at least one healthy shoot and attached roots, it should grow in its new location.